Problem: $ E = \left[\begin{array}{rrr}6 & 3 & 0 \\ 0 & 4 & 7 \\ 4 & 4 & 0\end{array}\right]$ What is $ E^{T}$ ?
Solution: To find the transpose, swap the rows and columns. $ E^{T}$ = $\left[\begin{array}{rrr}6 & 0 & 4 \\ 3 & 4 & 4 \\ 0 & 7 & 0\end{array}\right]$